<HTML>
<BODY BGCOLOR="white">
<PRE>
<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.analysis.solvers;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.NoBracketingException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.TooManyEvaluationsException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.NumberIsTooLargeException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.util.Precision;<a name="line.24"></a>
<FONT color="green">025</FONT>    <a name="line.25"></a>
<FONT color="green">026</FONT>    /**<a name="line.26"></a>
<FONT color="green">027</FONT>     * This class implements the &lt;a href="http://mathworld.wolfram.com/BrentsMethod.html"&gt;<a name="line.27"></a>
<FONT color="green">028</FONT>     * Brent algorithm&lt;/a&gt; for finding zeros of real univariate functions.<a name="line.28"></a>
<FONT color="green">029</FONT>     * The function should be continuous but not necessarily smooth.<a name="line.29"></a>
<FONT color="green">030</FONT>     * The {@code solve} method returns a zero {@code x} of the function {@code f}<a name="line.30"></a>
<FONT color="green">031</FONT>     * in the given interval {@code [a, b]} to within a tolerance<a name="line.31"></a>
<FONT color="green">032</FONT>     * {@code 6 eps abs(x) + t} where {@code eps} is the relative accuracy and<a name="line.32"></a>
<FONT color="green">033</FONT>     * {@code t} is the absolute accuracy.<a name="line.33"></a>
<FONT color="green">034</FONT>     * The given interval must bracket the root.<a name="line.34"></a>
<FONT color="green">035</FONT>     *<a name="line.35"></a>
<FONT color="green">036</FONT>     * @version $Id: BrentSolver.java 1379560 2012-08-31 19:40:30Z erans $<a name="line.36"></a>
<FONT color="green">037</FONT>     */<a name="line.37"></a>
<FONT color="green">038</FONT>    public class BrentSolver extends AbstractUnivariateSolver {<a name="line.38"></a>
<FONT color="green">039</FONT>    <a name="line.39"></a>
<FONT color="green">040</FONT>        /** Default absolute accuracy. */<a name="line.40"></a>
<FONT color="green">041</FONT>        private static final double DEFAULT_ABSOLUTE_ACCURACY = 1e-6;<a name="line.41"></a>
<FONT color="green">042</FONT>    <a name="line.42"></a>
<FONT color="green">043</FONT>        /**<a name="line.43"></a>
<FONT color="green">044</FONT>         * Construct a solver with default accuracy (1e-6).<a name="line.44"></a>
<FONT color="green">045</FONT>         */<a name="line.45"></a>
<FONT color="green">046</FONT>        public BrentSolver() {<a name="line.46"></a>
<FONT color="green">047</FONT>            this(DEFAULT_ABSOLUTE_ACCURACY);<a name="line.47"></a>
<FONT color="green">048</FONT>        }<a name="line.48"></a>
<FONT color="green">049</FONT>        /**<a name="line.49"></a>
<FONT color="green">050</FONT>         * Construct a solver.<a name="line.50"></a>
<FONT color="green">051</FONT>         *<a name="line.51"></a>
<FONT color="green">052</FONT>         * @param absoluteAccuracy Absolute accuracy.<a name="line.52"></a>
<FONT color="green">053</FONT>         */<a name="line.53"></a>
<FONT color="green">054</FONT>        public BrentSolver(double absoluteAccuracy) {<a name="line.54"></a>
<FONT color="green">055</FONT>            super(absoluteAccuracy);<a name="line.55"></a>
<FONT color="green">056</FONT>        }<a name="line.56"></a>
<FONT color="green">057</FONT>        /**<a name="line.57"></a>
<FONT color="green">058</FONT>         * Construct a solver.<a name="line.58"></a>
<FONT color="green">059</FONT>         *<a name="line.59"></a>
<FONT color="green">060</FONT>         * @param relativeAccuracy Relative accuracy.<a name="line.60"></a>
<FONT color="green">061</FONT>         * @param absoluteAccuracy Absolute accuracy.<a name="line.61"></a>
<FONT color="green">062</FONT>         */<a name="line.62"></a>
<FONT color="green">063</FONT>        public BrentSolver(double relativeAccuracy,<a name="line.63"></a>
<FONT color="green">064</FONT>                           double absoluteAccuracy) {<a name="line.64"></a>
<FONT color="green">065</FONT>            super(relativeAccuracy, absoluteAccuracy);<a name="line.65"></a>
<FONT color="green">066</FONT>        }<a name="line.66"></a>
<FONT color="green">067</FONT>        /**<a name="line.67"></a>
<FONT color="green">068</FONT>         * Construct a solver.<a name="line.68"></a>
<FONT color="green">069</FONT>         *<a name="line.69"></a>
<FONT color="green">070</FONT>         * @param relativeAccuracy Relative accuracy.<a name="line.70"></a>
<FONT color="green">071</FONT>         * @param absoluteAccuracy Absolute accuracy.<a name="line.71"></a>
<FONT color="green">072</FONT>         * @param functionValueAccuracy Function value accuracy.<a name="line.72"></a>
<FONT color="green">073</FONT>         */<a name="line.73"></a>
<FONT color="green">074</FONT>        public BrentSolver(double relativeAccuracy,<a name="line.74"></a>
<FONT color="green">075</FONT>                           double absoluteAccuracy,<a name="line.75"></a>
<FONT color="green">076</FONT>                           double functionValueAccuracy) {<a name="line.76"></a>
<FONT color="green">077</FONT>            super(relativeAccuracy, absoluteAccuracy, functionValueAccuracy);<a name="line.77"></a>
<FONT color="green">078</FONT>        }<a name="line.78"></a>
<FONT color="green">079</FONT>    <a name="line.79"></a>
<FONT color="green">080</FONT>        /**<a name="line.80"></a>
<FONT color="green">081</FONT>         * {@inheritDoc}<a name="line.81"></a>
<FONT color="green">082</FONT>         */<a name="line.82"></a>
<FONT color="green">083</FONT>        @Override<a name="line.83"></a>
<FONT color="green">084</FONT>        protected double doSolve()<a name="line.84"></a>
<FONT color="green">085</FONT>            throws NoBracketingException,<a name="line.85"></a>
<FONT color="green">086</FONT>                   TooManyEvaluationsException,<a name="line.86"></a>
<FONT color="green">087</FONT>                   NumberIsTooLargeException {<a name="line.87"></a>
<FONT color="green">088</FONT>            double min = getMin();<a name="line.88"></a>
<FONT color="green">089</FONT>            double max = getMax();<a name="line.89"></a>
<FONT color="green">090</FONT>            final double initial = getStartValue();<a name="line.90"></a>
<FONT color="green">091</FONT>            final double functionValueAccuracy = getFunctionValueAccuracy();<a name="line.91"></a>
<FONT color="green">092</FONT>    <a name="line.92"></a>
<FONT color="green">093</FONT>            verifySequence(min, initial, max);<a name="line.93"></a>
<FONT color="green">094</FONT>    <a name="line.94"></a>
<FONT color="green">095</FONT>            // Return the initial guess if it is good enough.<a name="line.95"></a>
<FONT color="green">096</FONT>            double yInitial = computeObjectiveValue(initial);<a name="line.96"></a>
<FONT color="green">097</FONT>            if (FastMath.abs(yInitial) &lt;= functionValueAccuracy) {<a name="line.97"></a>
<FONT color="green">098</FONT>                return initial;<a name="line.98"></a>
<FONT color="green">099</FONT>            }<a name="line.99"></a>
<FONT color="green">100</FONT>    <a name="line.100"></a>
<FONT color="green">101</FONT>            // Return the first endpoint if it is good enough.<a name="line.101"></a>
<FONT color="green">102</FONT>            double yMin = computeObjectiveValue(min);<a name="line.102"></a>
<FONT color="green">103</FONT>            if (FastMath.abs(yMin) &lt;= functionValueAccuracy) {<a name="line.103"></a>
<FONT color="green">104</FONT>                return min;<a name="line.104"></a>
<FONT color="green">105</FONT>            }<a name="line.105"></a>
<FONT color="green">106</FONT>    <a name="line.106"></a>
<FONT color="green">107</FONT>            // Reduce interval if min and initial bracket the root.<a name="line.107"></a>
<FONT color="green">108</FONT>            if (yInitial * yMin &lt; 0) {<a name="line.108"></a>
<FONT color="green">109</FONT>                return brent(min, initial, yMin, yInitial);<a name="line.109"></a>
<FONT color="green">110</FONT>            }<a name="line.110"></a>
<FONT color="green">111</FONT>    <a name="line.111"></a>
<FONT color="green">112</FONT>            // Return the second endpoint if it is good enough.<a name="line.112"></a>
<FONT color="green">113</FONT>            double yMax = computeObjectiveValue(max);<a name="line.113"></a>
<FONT color="green">114</FONT>            if (FastMath.abs(yMax) &lt;= functionValueAccuracy) {<a name="line.114"></a>
<FONT color="green">115</FONT>                return max;<a name="line.115"></a>
<FONT color="green">116</FONT>            }<a name="line.116"></a>
<FONT color="green">117</FONT>    <a name="line.117"></a>
<FONT color="green">118</FONT>            // Reduce interval if initial and max bracket the root.<a name="line.118"></a>
<FONT color="green">119</FONT>            if (yInitial * yMax &lt; 0) {<a name="line.119"></a>
<FONT color="green">120</FONT>                return brent(initial, max, yInitial, yMax);<a name="line.120"></a>
<FONT color="green">121</FONT>            }<a name="line.121"></a>
<FONT color="green">122</FONT>    <a name="line.122"></a>
<FONT color="green">123</FONT>            throw new NoBracketingException(min, max, yMin, yMax);<a name="line.123"></a>
<FONT color="green">124</FONT>        }<a name="line.124"></a>
<FONT color="green">125</FONT>    <a name="line.125"></a>
<FONT color="green">126</FONT>        /**<a name="line.126"></a>
<FONT color="green">127</FONT>         * Search for a zero inside the provided interval.<a name="line.127"></a>
<FONT color="green">128</FONT>         * This implementation is based on the algorithm described at page 58 of<a name="line.128"></a>
<FONT color="green">129</FONT>         * the book<a name="line.129"></a>
<FONT color="green">130</FONT>         * &lt;quote&gt;<a name="line.130"></a>
<FONT color="green">131</FONT>         *  &lt;b&gt;Algorithms for Minimization Without Derivatives&lt;/b&gt;<a name="line.131"></a>
<FONT color="green">132</FONT>         *  &lt;it&gt;Richard P. Brent&lt;/it&gt;<a name="line.132"></a>
<FONT color="green">133</FONT>         *  Dover 0-486-41998-3<a name="line.133"></a>
<FONT color="green">134</FONT>         * &lt;/quote&gt;<a name="line.134"></a>
<FONT color="green">135</FONT>         *<a name="line.135"></a>
<FONT color="green">136</FONT>         * @param lo Lower bound of the search interval.<a name="line.136"></a>
<FONT color="green">137</FONT>         * @param hi Higher bound of the search interval.<a name="line.137"></a>
<FONT color="green">138</FONT>         * @param fLo Function value at the lower bound of the search interval.<a name="line.138"></a>
<FONT color="green">139</FONT>         * @param fHi Function value at the higher bound of the search interval.<a name="line.139"></a>
<FONT color="green">140</FONT>         * @return the value where the function is zero.<a name="line.140"></a>
<FONT color="green">141</FONT>         */<a name="line.141"></a>
<FONT color="green">142</FONT>        private double brent(double lo, double hi,<a name="line.142"></a>
<FONT color="green">143</FONT>                             double fLo, double fHi) {<a name="line.143"></a>
<FONT color="green">144</FONT>            double a = lo;<a name="line.144"></a>
<FONT color="green">145</FONT>            double fa = fLo;<a name="line.145"></a>
<FONT color="green">146</FONT>            double b = hi;<a name="line.146"></a>
<FONT color="green">147</FONT>            double fb = fHi;<a name="line.147"></a>
<FONT color="green">148</FONT>            double c = a;<a name="line.148"></a>
<FONT color="green">149</FONT>            double fc = fa;<a name="line.149"></a>
<FONT color="green">150</FONT>            double d = b - a;<a name="line.150"></a>
<FONT color="green">151</FONT>            double e = d;<a name="line.151"></a>
<FONT color="green">152</FONT>    <a name="line.152"></a>
<FONT color="green">153</FONT>            final double t = getAbsoluteAccuracy();<a name="line.153"></a>
<FONT color="green">154</FONT>            final double eps = getRelativeAccuracy();<a name="line.154"></a>
<FONT color="green">155</FONT>    <a name="line.155"></a>
<FONT color="green">156</FONT>            while (true) {<a name="line.156"></a>
<FONT color="green">157</FONT>                if (FastMath.abs(fc) &lt; FastMath.abs(fb)) {<a name="line.157"></a>
<FONT color="green">158</FONT>                    a = b;<a name="line.158"></a>
<FONT color="green">159</FONT>                    b = c;<a name="line.159"></a>
<FONT color="green">160</FONT>                    c = a;<a name="line.160"></a>
<FONT color="green">161</FONT>                    fa = fb;<a name="line.161"></a>
<FONT color="green">162</FONT>                    fb = fc;<a name="line.162"></a>
<FONT color="green">163</FONT>                    fc = fa;<a name="line.163"></a>
<FONT color="green">164</FONT>                }<a name="line.164"></a>
<FONT color="green">165</FONT>    <a name="line.165"></a>
<FONT color="green">166</FONT>                final double tol = 2 * eps * FastMath.abs(b) + t;<a name="line.166"></a>
<FONT color="green">167</FONT>                final double m = 0.5 * (c - b);<a name="line.167"></a>
<FONT color="green">168</FONT>    <a name="line.168"></a>
<FONT color="green">169</FONT>                if (FastMath.abs(m) &lt;= tol ||<a name="line.169"></a>
<FONT color="green">170</FONT>                    Precision.equals(fb, 0))  {<a name="line.170"></a>
<FONT color="green">171</FONT>                    return b;<a name="line.171"></a>
<FONT color="green">172</FONT>                }<a name="line.172"></a>
<FONT color="green">173</FONT>                if (FastMath.abs(e) &lt; tol ||<a name="line.173"></a>
<FONT color="green">174</FONT>                    FastMath.abs(fa) &lt;= FastMath.abs(fb)) {<a name="line.174"></a>
<FONT color="green">175</FONT>                    // Force bisection.<a name="line.175"></a>
<FONT color="green">176</FONT>                    d = m;<a name="line.176"></a>
<FONT color="green">177</FONT>                    e = d;<a name="line.177"></a>
<FONT color="green">178</FONT>                } else {<a name="line.178"></a>
<FONT color="green">179</FONT>                    double s = fb / fa;<a name="line.179"></a>
<FONT color="green">180</FONT>                    double p;<a name="line.180"></a>
<FONT color="green">181</FONT>                    double q;<a name="line.181"></a>
<FONT color="green">182</FONT>                    // The equality test (a == c) is intentional,<a name="line.182"></a>
<FONT color="green">183</FONT>                    // it is part of the original Brent's method and<a name="line.183"></a>
<FONT color="green">184</FONT>                    // it should NOT be replaced by proximity test.<a name="line.184"></a>
<FONT color="green">185</FONT>                    if (a == c) {<a name="line.185"></a>
<FONT color="green">186</FONT>                        // Linear interpolation.<a name="line.186"></a>
<FONT color="green">187</FONT>                        p = 2 * m * s;<a name="line.187"></a>
<FONT color="green">188</FONT>                        q = 1 - s;<a name="line.188"></a>
<FONT color="green">189</FONT>                    } else {<a name="line.189"></a>
<FONT color="green">190</FONT>                        // Inverse quadratic interpolation.<a name="line.190"></a>
<FONT color="green">191</FONT>                        q = fa / fc;<a name="line.191"></a>
<FONT color="green">192</FONT>                        final double r = fb / fc;<a name="line.192"></a>
<FONT color="green">193</FONT>                        p = s * (2 * m * q * (q - r) - (b - a) * (r - 1));<a name="line.193"></a>
<FONT color="green">194</FONT>                        q = (q - 1) * (r - 1) * (s - 1);<a name="line.194"></a>
<FONT color="green">195</FONT>                    }<a name="line.195"></a>
<FONT color="green">196</FONT>                    if (p &gt; 0) {<a name="line.196"></a>
<FONT color="green">197</FONT>                        q = -q;<a name="line.197"></a>
<FONT color="green">198</FONT>                    } else {<a name="line.198"></a>
<FONT color="green">199</FONT>                        p = -p;<a name="line.199"></a>
<FONT color="green">200</FONT>                    }<a name="line.200"></a>
<FONT color="green">201</FONT>                    s = e;<a name="line.201"></a>
<FONT color="green">202</FONT>                    e = d;<a name="line.202"></a>
<FONT color="green">203</FONT>                    if (p &gt;= 1.5 * m * q - FastMath.abs(tol * q) ||<a name="line.203"></a>
<FONT color="green">204</FONT>                        p &gt;= FastMath.abs(0.5 * s * q)) {<a name="line.204"></a>
<FONT color="green">205</FONT>                        // Inverse quadratic interpolation gives a value<a name="line.205"></a>
<FONT color="green">206</FONT>                        // in the wrong direction, or progress is slow.<a name="line.206"></a>
<FONT color="green">207</FONT>                        // Fall back to bisection.<a name="line.207"></a>
<FONT color="green">208</FONT>                        d = m;<a name="line.208"></a>
<FONT color="green">209</FONT>                        e = d;<a name="line.209"></a>
<FONT color="green">210</FONT>                    } else {<a name="line.210"></a>
<FONT color="green">211</FONT>                        d = p / q;<a name="line.211"></a>
<FONT color="green">212</FONT>                    }<a name="line.212"></a>
<FONT color="green">213</FONT>                }<a name="line.213"></a>
<FONT color="green">214</FONT>                a = b;<a name="line.214"></a>
<FONT color="green">215</FONT>                fa = fb;<a name="line.215"></a>
<FONT color="green">216</FONT>    <a name="line.216"></a>
<FONT color="green">217</FONT>                if (FastMath.abs(d) &gt; tol) {<a name="line.217"></a>
<FONT color="green">218</FONT>                    b += d;<a name="line.218"></a>
<FONT color="green">219</FONT>                } else if (m &gt; 0) {<a name="line.219"></a>
<FONT color="green">220</FONT>                    b += tol;<a name="line.220"></a>
<FONT color="green">221</FONT>                } else {<a name="line.221"></a>
<FONT color="green">222</FONT>                    b -= tol;<a name="line.222"></a>
<FONT color="green">223</FONT>                }<a name="line.223"></a>
<FONT color="green">224</FONT>                fb = computeObjectiveValue(b);<a name="line.224"></a>
<FONT color="green">225</FONT>                if ((fb &gt; 0 &amp;&amp; fc &gt; 0) ||<a name="line.225"></a>
<FONT color="green">226</FONT>                    (fb &lt;= 0 &amp;&amp; fc &lt;= 0)) {<a name="line.226"></a>
<FONT color="green">227</FONT>                    c = a;<a name="line.227"></a>
<FONT color="green">228</FONT>                    fc = fa;<a name="line.228"></a>
<FONT color="green">229</FONT>                    d = b - a;<a name="line.229"></a>
<FONT color="green">230</FONT>                    e = d;<a name="line.230"></a>
<FONT color="green">231</FONT>                }<a name="line.231"></a>
<FONT color="green">232</FONT>            }<a name="line.232"></a>
<FONT color="green">233</FONT>        }<a name="line.233"></a>
<FONT color="green">234</FONT>    }<a name="line.234"></a>




























































</PRE>
</BODY>
</HTML>
